Current, no current, shallow, deep, it's all the same (just like bank and boat fishing...)
The goal is to present your lure wherever they are. Sure, the current will play a big role on where the fish will be, and you need to figure that out, but once you have done that, use the lure best gets to that spot. A lure will look more natural, and fish are more often than not conditioned to have prey swept down current to them, so yes, casting upstream and retrieving with the current or quartering it will usually be more productive, as can just following the lure downstream on a semi slack line.